I did some research. Apparently, pulp fiction is the style of writing very stylized from the 40's and 50's. It usually is told in first person with the main character getting it in the head repeatedly. Pulps were very popular before TV. So "newPulp" is anything written in the style but not the old Pulp Fiction. Plus, it differentiates itself from the movie by the same name. Your cowboy story seems to be new pulp in that it hearkens back to the pulp form. Pulp fiction was anything on the newsstand from westerns, mysteries, romance, sci-fi, etc. It rarely went over 6-10,000 words and could be read on the bus.